Dynamic compensation, parameter identifiability, and equivariances

A recent paper by Karin, Swisa, Glaser, Dor, and Alon introduced the mathematical notion of dynamical compensation (DC) in biological circuits, arguing that DC helps explain important features of glucose homeostasis as well as other key physiological regulatory mechanisms. The present paper establishes a connection between DC and two well-known notions in systems biology: system equivalence and parameter (un)identifiability. This recasting leads to effective tests for verifying DC in mathematical models.